Vector Bundles on Rational Topologically Contractible Affine Threefolds

Abstract

The generalized Serre question asks whether any algebraic vector bundle over a topologically contractible, smooth, affine, complex variety $X$ is trivial. In this article, we prove an affirmative answer to this question, if the dimension of $X$ is 3 and $X$ is rationally connected. As an example, this proves that every algebraic vector bundle over any Koras-Russell threefold (first or second kind and certain third kind) is trivial.